1 Introduction

This paper contains estimates for the effective reproduction number \(R_{t,m}\) over time \(t\) in various nations and other regions \(m\) of United Kingdom. This is done using the methodology as described in [1]. These have been implemented in R using EpiEstim package [2] which is what is used here. The methodolgy and assumptions are described in more detail here.

This paper and it’s results should be updated roughly daily and is available online.

As this paper is updated over time this section will summarise significant changes. The code producing this paper is tracked using Git. The Git commit hash for this project at the time of generating this paper was 687710471b373ff5d19f908e5acb0fc83984dc1d.

2 Data

Data is obtained [3]. This contains the daily cases, hospital admissions and deaths for United Kingdom by various geographies. Here the data is accessed by specimen date, admission date and date of death.

Once history is built up an allowance for rate reported cases, admissions and deaths will be made. For now the data is cut-off a week prior to the last case date in the data. All data prior to 1 March 2020 are removed.

3 Methodology

The methodology is described in detail here.

4 Results by Nation

4.1 Cases

Below we plot cumulative case count on a log scale by nation:

Cumulative Cases by Nation

Cumulative Cases by Nation

4.2 Admissions

Below we plot cumulative hospital admissions on a log scale.

Cumulative Admissions by Nation

Cumulative Admissions by Nation

4.3 Deaths

Below we plot the cumulative deaths by nation on a log scale:

Cumulative Deaths by Nation

Cumulative Deaths by Nation

4.4 Current \(R_{t,m}\) estimates by Nation

Below current (last weekly) \(R_{t,m}\) estimates are tabulated.

Estimated Effective Reproduction Number by Nation
Nation Estimate Type Count (Last Week) Week Ending R - Lower CI R - Mean R - Uppper CI
England cases 138,044 2020-11-04 1.1 1.1 1.1
England admissions 8,933 2020-11-04 1.1 1.1 1.1
England deaths 1,857 2020-11-04 1.1 1.2 1.3
Northern Ireland cases 4,439 2020-11-04 0.8 0.8 0.9
Northern Ireland admissions 317 2020-11-04 0.9 1.0 1.1
Northern Ireland deaths 67 2020-11-04 0.9 1.1 1.4
Scotland cases 8,097 2020-11-04 1.0 1.0 1.0
Scotland admissions 608 2020-11-04 0.8 0.9 0.9
Scotland deaths 197 2020-11-04 1.1 1.2 1.4
Wales cases 8,359 2020-11-04 0.9 1.0 1.0
Wales admissions 647 2020-11-04 0.9 1.0 1.1
Wales deaths 128 2020-11-04 0.9 1.1 1.3
Estimated Effective Reproduction Number by Nation

Estimated Effective Reproduction Number by Nation

4.5 Maps of Effective Reproduction Number

Below we plot the current effective reproduction number on maps with boundaries provided by [4].

4.5.1 Cases

4.5.2 Admissions

4.5.3 Deaths

4.6 Graphs over Time

Below we plot results for each nation We filter out weeks where the upper end of confidence interval for \(R_{t,m}\) exceeds 4.

4.6.1 England

4.6.2 Northern Ireland

4.6.3 Scotland

4.6.4 Wales

5 Results by Region

5.1 Cases

Below we plot cumulative case count on a log scale by region:

Cumulative Cases by Region

Cumulative Cases by Region

5.2 Deaths

Below we plot the cumulative deaths by region on a log scale:

Cumulative Deaths by Region

Cumulative Deaths by Region

5.3 Current \(R_{t,m}\) estimates by Region

Below current (last weekly) \(R_{t,m}\) estimates are tabulated.

Estimated Effective Reproduction Number by Region
Region Estimate Type Count (Last Week) Week Ending R - Lower CI R - Mean R - Uppper CI
Northern Ireland cases 4,439 2020-11-04 0.8 0.8 0.9
Northern Ireland deaths 67 2020-11-04 0.9 1.1 1.4
Scotland cases 8,097 2020-11-04 1.0 1.0 1.0
Scotland deaths 197 2020-11-04 1.1 1.2 1.4
Wales cases 8,359 2020-11-04 0.9 1.0 1.0
Wales deaths 128 2020-11-04 0.9 1.1 1.3
East Midlands cases 14,572 2020-11-04 1.1 1.1 1.1
East Midlands deaths 198 2020-11-04 1.1 1.2 1.4
East of England cases 6,926 2020-11-04 1.1 1.1 1.1
East of England deaths 111 2020-11-04 1.0 1.2 1.5
London cases 13,565 2020-11-04 1.0 1.0 1.0
London deaths 90 2020-11-04 0.9 1.1 1.3
North East cases 8,770 2020-11-04 1.1 1.1 1.1
North East deaths 137 2020-11-04 0.9 1.1 1.2
North West cases 29,493 2020-11-04 1.0 1.0 1.0
North West deaths 586 2020-11-04 1.1 1.1 1.2
South East cases 12,043 2020-11-04 1.1 1.1 1.2
South East deaths 111 2020-11-04 1.1 1.4 1.7
South West cases 8,978 2020-11-04 1.1 1.1 1.1
South West deaths 67 2020-11-04 0.9 1.1 1.4
West Midlands cases 18,064 2020-11-04 1.1 1.2 1.2
West Midlands deaths 211 2020-11-04 1.1 1.3 1.5
Yorkshire and The Humber cases 24,423 2020-11-04 1.1 1.1 1.1
Yorkshire and The Humber deaths 323 2020-11-04 1.1 1.3 1.4
Estimated Effective Reproduction Number by Region

Estimated Effective Reproduction Number by Region

5.4 Maps of Effective Reproduction Number

Below we plot the current effective reproduction number on maps with boundaries provided by [5].

5.4.1 Cases

5.4.2 Deaths

5.5 Graphs over Time

Below we plot results for each nation We filter out weeks where the upper end of confidence interval for \(R_{t,m}\) exceeds 4.

5.5.1 Northern Ireland

5.5.2 Scotland

5.5.3 Wales

5.5.4 East Midlands

5.5.5 East of England

5.5.6 London

5.5.7 North East

5.5.8 North West

5.5.9 South East

5.5.10 South West

5.5.11 West Midlands

5.5.12 Yorkshire and The Humber

6 Results by NHS Region

6.1 Current \(R_{t,m}\) estimates by Region

Below current (last weekly) \(R_{t,m}\) estimates are tabulated.

Estimated Effective Reproduction Number by Region
Region Estimate Type Count (Last Week) Week Ending R - Lower CI R - Mean R - Uppper CI
Northern Ireland admissions 317 2020-11-04 0.9 1.0 1.1
Scotland admissions 608 2020-11-04 0.8 0.9 0.9
Wales admissions 647 2020-11-04 0.9 1.0 1.1
East of England admissions 476 2020-11-04 1.1 1.2 1.3
London admissions 894 2020-11-04 1.0 1.0 1.1
North West admissions 2,046 2020-11-04 1.0 1.0 1.0
South East admissions 678 2020-11-04 1.1 1.2 1.3
South West admissions 603 2020-11-04 1.2 1.3 1.4
Midlands admissions 1,889 2020-11-04 1.1 1.1 1.2
North East and Yorkshire admissions 2,347 2020-11-04 1.1 1.1 1.2
Estimated Effective Reproduction Number by Region

Estimated Effective Reproduction Number by Region

6.2 Maps of Effective Reproduction Number

Below we plot the current effective reproduction number on maps with boundaries provided by [6].

6.3 Graphs over Time

Below we plot results for each nation We filter out weeks where the upper end of confidence interval for \(R_{t,m}\) exceeds 4.

6.3.1 East of England

6.3.2 London

6.3.3 Midlands

6.3.4 North East and Yorkshire

6.3.5 North West

6.3.6 South East

6.3.7 South West

7 Results by Upper Tier Local Authority

7.1 Highest \(R_{t,m}\) as estimated using cases

Below we plot Upper Tier Local Authorities with the hghest reproduction numbers (providing they had at least 100 cases):

## Selecting by Rt_ui_95
Estimated Effective Reproduction Number by Upper Tier Local Authority
Upper Tier Local Authority Estimate Type Count (Last Week) Week Ending R - Lower CI R - Mean R - Uppper CI
Inverclyde cases 114 2020-11-04 1.3 1.6 2.0
Kingston upon Hull, City of cases 1,654 2020-11-04 1.4 1.6 1.7
Stirling cases 118 2020-11-04 1.3 1.5 1.8
Torbay cases 301 2020-11-04 1.2 1.4 1.6
North East Lincolnshire cases 978 2020-11-04 1.3 1.4 1.5
Kent cases 2,214 2020-11-04 1.3 1.3 1.4
Medway cases 482 2020-11-04 1.2 1.3 1.5
Dudley cases 1,392 2020-11-04 1.2 1.3 1.4
North Somerset cases 493 2020-11-04 1.2 1.3 1.4
North Lincolnshire cases 534 2020-11-04 1.2 1.3 1.4
Redcar and Cleveland cases 501 2020-11-04 1.2 1.3 1.4
Worcestershire cases 1,228 2020-11-04 1.2 1.3 1.4
East Riding of Yorkshire cases 1,303 2020-11-04 1.2 1.3 1.4
Central Bedfordshire cases 340 2020-11-04 1.2 1.3 1.4
Somerset cases 550 2020-11-04 1.2 1.3 1.4
Northamptonshire cases 1,336 2020-11-04 1.2 1.3 1.3
South Tyneside cases 461 2020-11-04 1.2 1.3 1.4
Havering cases 657 2020-11-04 1.2 1.3 1.4
Luton cases 548 2020-11-04 1.2 1.3 1.4
Bexley cases 452 2020-11-04 1.2 1.3 1.4
Gloucestershire cases 815 2020-11-04 1.2 1.3 1.4
Fife cases 378 2020-11-04 1.1 1.2 1.4
Vale of Glamorgan cases 218 2020-11-04 1.1 1.2 1.4
West Berkshire cases 168 2020-11-04 1.0 1.2 1.4
Perth and Kinross cases 130 2020-11-04 1.0 1.2 1.4

7.2 Map of Effective Reproduction Number (Cases)

Below we plot the current effective reproduction number estimated from case data on maps with boundaries provided by [7].

7.3 Map over by week since start of the year (experimental)

Below the reproduction number by week for each Upper Tier Local Authority is animated:

8 Detailed Results

Detailed output are saved to a comma-separated value file. The file can be found here.

9 Discussion

Limitation of this method to estimate \(R_{t,m}\) are noted in [1]

  • It’s sensitive to changes in transmissibility, changes in contact patterns, depletion of the susceptible population and control measures.
  • It relies on an assumed generation interval assumptions.
  • The size of the time window can affect the volatility of results.
  • Results are time lagged with regards to true infection, more so in the case of the use of deaths.
  • It’s sensitive to changes in case (or death) detection.
  • The generation interval may change over time.

Further to the above the estimates are made under assumption that the cases and deaths are reported consistently over time. For cases this means that testing needs to be at similar levels and reported with similar lag. Should these change rapidly over an interval of a few weeks the above estimates of the effective reproduction numbers would be biased. For example a rapid expansion of testing over the last 3 weeks would results in overestimating recent effective reproduction numbers. Similarly any changes in reporting (over time and underreporting) of deaths would also bias estimates of the reproduction number estimated using deaths. It may well be that some catch-up in reported deaths is exaggerating the estimates for October.

Estimates for the reproduction number are plotted in time period in which the relevant measure is recorded. Though in reality the infections giving rise to those estimates would have occurred roughly between a week to 4 weeks earlier depending on whether it was cases or deaths. These figures have not been shifted back.

Despite these limitation we believe the ease of calculation of this method and the ability to use multiple sources makes it useful as a monitoring tool.

Having said all the above it would appear that the effective reproduction number was reasonably high in United Kingdom from middle April to middle July. From middle July the figures seems to have decreased well below 1. However since middle September figures have been near 1 and in October these seem to have shifted above 1.

10 Author

This report was prepared by Louis Rossouw. Please get in contact with Louis Rossouw if you have comments or wish to receive this regularly.

Louis Rossouw
Head of Research & Analytics
Gen Re | Life/Health Canada, South Africa, Australia, NZ, UK & Ireland
Email: LRossouw@GenRe.com Mobile: +27 71 355 2550

The views in this document represents that of the author and may not represent those of Gen Re. Also note that given the significant uncertainty involved with the parameters, data and methodology care should be taken with these numbers and any use of these numbers.

11 Digital boundaries

Office for National Statistics licensed under the Open Government Licence v.3.0

Contains OS data © Crown copyright and database right 2020

References

[1] A. Cori, N. M. Ferguson, C. Fraser, and S. Cauchemez, “A new framework and software to estimate time-varying reproduction numbers during epidemics,” American Journal of Epidemiology, vol. 178, no. 9, pp. 1505–1512, Sep. 2013, doi: 10.1093/aje/kwt133. [Online]. Available: https://doi.org/10.1093/aje/kwt133

[2] A. Cori, EpiEstim: A package to estimate time varying reproduction numbers from epidemic curves. 2013 [Online]. Available: https://CRAN.R-project.org/package=EpiEstim

[3] Office for National Statistics, “Official UK Coronavirus Dashboard,” 2020. [Online]. Available: https://coronavirus.data.gov.uk. [Accessed: 07-Nov-2020]

[4] Office for National Statistics, “Countries (December 2019) Boundaries UK BUC,” 09-Oct-2017. [Online]. Available: https://geoportal.statistics.gov.uk/search?collection=Dataset. [Accessed: 07-Nov-2020]

[5] Office for National Statistics, “NUTS Level 1 (January 2018) Ultra Generalised Clipped Boundaries in the United Kingdom,” 31-Jul-2017. [Online]. Available: https://geoportal.statistics.gov.uk/datasets/nuts-level-1-january-2018-ultra-generalised-clipped-boundaries-in-the-united-kingdom. [Accessed: 07-Nov-2020]

[6] Office for National Statistics, “NHS England Regions (April 2020) Boundaries EN BUC,” 13-May-2020. [Online]. Available: https://geoportal.statistics.gov.uk/search?collection=Dataset. [Accessed: 07-Nov-2020]

[7] Office for National Statistics, “Counties and Unitary Authorities (December 2019) Boundaries UK BUC,” 11-Mar-2020. [Online]. Available: https://geoportal.statistics.gov.uk/datasets/counties-and-unitary-authorities-december-2019-boundaries-uk-buc. [Accessed: 07-Nov-2020]